Choose the king and then drag it to the destination square like you would
if you were playing with a physical set. Or touch the king to select the piece and then touch the destination square.
If that was what you were trying you should verify that all castling rules were met.
A castling move cannot be made if ether the king or the rook has been moved once. Although that only counts for the rook moved. So if you had moved your kingside room you could still castle on the queenside, assuming that rook and your king have not been touched. Also you cannot castle out of check, into check, or through check.
I assume this is the game, as it's the only one I can find in your history - http://www.chess.com/echess/game?id=117420418
In this case you moved your queenside rook on move 10, which would rule out castling on that side of the board. From move 16 black's rook is attacking the g1 square and blocking you from castling on the kingside. That block lasts until move 23, when you take the rook with your h file Pawn. But then from move 24 black's bishop is sitting on the d4 square, attacking the g1 square and blocking the castling move. And on move 26 you've moved your h flie rook, which takes away the ability to castle kingside even if you had returned the rook to the h1 square.
Hope this helps.
Please help me as the app wouldn't accept my Castling move